ExpertHard3 marksStructured
AQA GCSE · Question 17.4 · Statistical Measures and Calculations
Jim says,
“The index number for CPI is 120 to the nearest whole number for May 2018 with Jan 2010 as base.
So the index number for CPI for Jan 2010 with May 2018 as base will be 80 to the nearest whole number.”
Evaluate all of Jim’s statement. Use calculations, where necessary, to show if he is correct.
Jim says,
“The index number for CPI is 120 to the nearest whole number for May 2018 with Jan 2010 as base.
So the index number for CPI for Jan 2010 with May 2018 as base will be 80 to the nearest whole number.”
Evaluate all of Jim’s statement. Use calculations, where necessary, to show if he is correct.
How to approach this question
Jim's statement has two parts. The first is an observation. The second is a calculation based on that observation. You need to check if his calculation is correct. The process is called "rebasing an index". The formula is: New Index = (Old Value / New Base Value) * 100.
1. Identify the "Old Value" (the index for Jan 2010).
2. Identify the "New Base Value" (the index for May 2018).
3. Substitute these into the formula and calculate the new index for Jan 2010.
4. Compare your result to Jim's claim of 80.
Full Answer
We need to evaluate the second part of Jim's statement by calculation. He is changing the base period of the index from Jan 2010 to May 2018.
The original index values are:
- Index for Jan 2010 (old base) = 100
- Index for May 2018 (new base) = 120
To rebase the index so that May 2018 = 100, we use the formula:
New Index = (Value in old index / Value of new base period in old index) × 100
We want to find the new index for Jan 2010.
- Value in old index (for Jan 2010) = 100
- Value of new base period (May 2018) in old index = 120
New Index for Jan 2010 = (100 / 120) × 100
New Index for Jan 2010 = (5 / 6) × 100
New Index for Jan 2010 = 83.33...
Rounding this to the nearest whole number gives 83.
Jim claimed the new index number would be 80. Our calculation shows it is 83.
Therefore, Jim is incorrect.
Common mistakes
✗ Incorrectly setting up the rebasing calculation, e.g., (120/100)*100 or 100 - 20 = 80. The relationship is multiplicative, not additive.
✗ Making a calculation error.
✗ Correctly calculating 83 but failing to state clearly that Jim is incorrect.
Practice the full AQA GCSE Statistics Foundation Tier Paper 1
47 questions · hints · full answers · grading
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